\noindent Modern technology scaling enables integration of billions of
transistors on the same chip. This increase in design complexity makes it
difficult to comprehensively validate the design prior to mass
production. Post-silicon validation schemes are also pressed by tight
time-to-market requirements.  The main challenge in post-silicon validation
is the lack of observability to the internal signals of the manufactured
chips. One way to increase this observability is by using Embedded Logic
Analyzers (ELAs) which are widely adopted by the industry for the past few
years. A core component inside an ELA are trace buffers. Trace buffers
record the signal values corresponding to a small subset of state elements
in the design for an observation window of about few thousand clock
cycles. Due to the large area overhead of the trace buffers, only a small
fraction of the state elements in the design can be traced online. The
signal values of the traced state elements within the observation window
are then used to restore the values of the remaining not-traced state
elements. The automated trace signal selection problem focuses on selection
of the trace signals in order to maximize the restoration of the remaining
state elements within the observation window.

In this dissertation, we first propose a hybrid single-mode trace signal
selection algorithm which achieves a good balance between solution quality
and runtime-scalability. Next, we consider the impact of control signals in
the restoration process using the values of the trace signals. We first
propose an automated procedure to identify control signals; currently
identification of control signals in a design is mostly done
manually. However manual identification is not an easy task anymore because
of increase in the number of control signals with increase in design
complexity as well as automated insertion by CAD tools. We next introduce
the trace signal selection problem in the presence of multiple operation
modes which occur when control signals take different values. We show
existing algorithms which are based on trace signal selection in a single
operation mode achieve poor signal restoration over multiple operation
modes. In contrast, our proposed algorithm considers restoration over all
the operation modes and is therefore able to achieve much higher
restoration over all the desired operation modes.